perplexus.info :: Just Math : Temperature Temperament IV

Temperature Temperament IV (Posted on 2022-01-03)

Find all possible pair(s) (A, B) of positive base 10 digits satisfying this relationship:

(B/A)^o Celsius = (AB)^o Fahrenheit, where AB denotes the concatenation of digits.

Provide valid reasoning for your answer.

*** It may be noted that F = (9/5)*C+32, wher C denotes degree(s) Celsius and F denotes degree(s) Fahrenheit.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 1 of 3

clearvars, clc

syms a b

for fahr=10:99

a=floor(fahr/10);

b=mod(fahr,10);

celsius=5*(sym(fahr-32))/9;

if a*celsius==b

disp([fahr celsius])

disp(double(celsius))

end

finds only that 35°F = 5/3 °C.

But if we extend so that B itself might be a concatenation of two digits, if B=85 and A=1, 185°F = 85/1 °C, from

clearvars, clc

syms a b

for fahr=10:999

a=floor(fahr/100);

b=mod(fahr,100);

celsius=5*(sym(fahr-32))/9;

if a*celsius==b

disp([fahr celsius])

disp(double(celsius))

end

Posted by Charlie on 2022-01-03 11:05:09

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